It’s not the OS, per se, but I was able to track the source back to the Gnome Toolkit (GTK). After disabling event sounds globally, I no longer get the sound from Atom.

This isn’t really a perfect solution, however. GTK applications don’t behave consistently in this regard. Most don’t trigger a sound for these types of dialogs. This leads me to believe that there’s something about the way that Atom/Electron calls the GTK API which causes the sound to happen.